A finite-length burst yields a short-lived autocorrelation that vanishes beyond its duration

Evidence

Autocorrelation is a check for repetition or self-similarity. Does the signal, which might look quite unruly, tend in fact to repeat patterns at regular intervals? For example, if there is a large positive fluctuation in s(t) at some time t, does there tend to be another a time τ later? Or, is it anticorrelated at time τ: most often s(t + τ) has the opposite sign as does s(t). The product s(t)s(t + τ) would be most often negative and 〈s(r)s(t + τ)〉 would be negative for that value of the time delay τ. If s(t) and s(t + τ) are uncorrelated, so that s(t)s(t + τ) is as likely positive as negative, the average and thus c(τ) will be zero at time τ. — Eric J. Heller, Why You Hear What You Hear- An…, 369 (#expands, via linked claim)

This works so well that tiny signals can be rescued from a lot of noise, as seen in figure 4.13. A pure noise signal and its autocorrelation are shown at the bottom. A noisy signal with a smooth periodic signal embedded appears at the top. The combined signal looks as ragged as the one at the bottom, which is pure noise. However, computing the autocorrelation reveals the hidden signal (top right). — Eric J. Heller, Why You Hear What You Hear- An…, 432 (#expands, via linked claim)

Categorization

• XREF: connects to: Tiny periodic signals can be recovered from heavy noise via autocorrelation — Eric J. Heller, Why You Hear What You Hear- An…, 432; Autocorrelation measures periodic self-similarity in a signal across time delays. — Eric J. Heller, Why You Hear What You Hear- An…, 369; A signal’s autocorrelation is a cosine sum over its sinusoidal partials.

Related

• Autocorrelation measures periodic self-similarity in a signal across time delays. (similarity 0.90)
• Tiny periodic signals can be recovered from heavy noise via autocorrelation (similarity 0.89)
• Autocorrelation discriminates echoes from genuine distinct sounds. (similarity 0.89)
• A signal’s autocorrelation is a cosine sum over its sinusoidal partials. (similarity 0.87)
• Impulse velocity response serves as a ready-made autocorrelation (similarity 0.85)
• Natural measurements correlate over time because dynamics persist (similarity 0.84)
• Temperature autocorrelation reveals weather’s daily and seasonal periodicities. (similarity 0.84)
• Correlograms track spike-train periodicity over time via sliding windows (similarity 0.83)
• Autocorrelation measures how a signal correlates with itself shifted in time (similarity 0.83)
• Autocorrelation reveals a signal’s fundamental periodicity through periodic peaks. (similarity 0.82)
• Time-delayed sound self-addition imposes spectral notches via autocorrelation (similarity 0.82)
• Autocorrelation is mathematically equivalent to the power spectrum (similarity 0.82)
• Autocorrelations are positive-coefficient cosine sums maximal at zero lag (similarity 0.82)
• Autocorrelation averages products across all shifted pairs (similarity 0.82)
• White noise has autocorrelation only at zero time shift. (similarity 0.81)

Broader Connections

• Autocorrelation measures periodic self-similarity in a signal across time delays. #expands (0.92) — Eric J. Heller, Why You Hear What You Hear- An…, 369
• Tiny periodic signals can be recovered from heavy noise via autocorrelation #expands (0.85) — Eric J. Heller, Why You Hear What You Hear- An…, 432
• A signal’s autocorrelation is a cosine sum over its sinusoidal partials. #expands (0.80)